TRURO's new-look Tesco store is piloting a scheme that means drivers will have to spend £5 to park there.
The superstore is one of only two among the chain's 3,000 in the UK to be trying the new parking system.
But the scheme has already come in for some criticism.
It is understood there will be a 15-minute 'grace period' and the measure is designed to prevent city centre shoppers using the supermarket as a free car park.
But a spokesman for Tesco would say only: "We always want to make sure our customers can find a parking space easily. This is why we've introduced a new parking system at our Truro store.
"We always welcome feedback from our customers and will monitor the new system to ensure that it's helping to free up spaces for those shoppers visiting the store."
Cameras scan customers' numberplates as they enter the car park. When they complete their shopping, they are given a voucher code which is inserted into a machine, removing the registration number from the system.
However, those failing to comply face a £70 fine.
The charge has been met with mixed feelings from city councillors.
Councillor Rob Nolan called the move "harsh and counterproductive.
"What if I want to linger for 45 minutes over a coffee and read the West Briton in the new coffee shop? That's £3.50. Will I be fined £70?
"We need Tesco to work in partnership with us. The town shops benefit from having Tesco close in, and Tesco benefit from the town.
"A two-hour maximum would have done the job."
Councillor Rosamund Cox said: "My husband is diabetic and has foot problems; if he goes in there for a cabbage or a couple of rolls he won't make it in 15 minutes."
Councillor Lorrie Eathorne-Gibbons said: "I do agree that people shouldn't park and go into town and use it as a free car park while visitors and residents pay parking fees, but in the current economic climate not everybody will spend more than £5."
Following completion of the refurbishment last week, store manager Stuart Bourn and his team will hold a relaunch ceremony at 10am on Monday and will present Truro Foodbank with a £500 donation.
